![bs01673_[1]](LO1%20Word%20Problems_files/image001.gif)
2.5 Problem Solving
How do you solve word problems?
Problem Solving Strategy
1. Analyze the problem
2. Form an equation
3. Solve the equation
4. State the conclusion
5. Check the result
Example:
A CD is priced at $15.00, but it is on sale for 20% off. What is the sale price of the CD?
1. Analyze the problem
Given: Original Price: $15.00 Discount: 20% off Unknown: x (sale price)
2. Form an equation
Original Price – Discount = Sale Price
15 - 0.20 (15) = x
3. Solve the equation
15 - 0.20 (15) = x
15 – 3 = x
x = 12
4. State the conclusion
The sale price of a CD that was $15.00 discount 20% is $12.00
5. Check the result
15 - 0.20 (15) = x
15 - 0.20 (15) = 12
15 – 3 = 12
12 = 12
Problems Solving Lab for MAT0024C
1. A pair of jeans is priced at $50.00, but is on sale for 25% off. What is the sale price of the pair of jeans?
a. $37.50
b. $40.00
c. $66.66
d. $12.50
2. If a television costs $311 after a 35% discount, what was the original cost?
a. $276.00
b. $419.85
c. $888.57
d. $478.46
3. If a DVD player costs $306 after a 30% increase in price, what was the original cost?
a. $91.80
b. $214.20
c. $437.14
d. $235.39
4. Find the amount of money now necessary to be invested at 5% simple interest to yield $200 interest in 8 years.
a. $125.00
b. $500.00
c. $320.00
d. $2500.00
5. The length of a rectangular garden is 8 more meters than its width. Its perimeter is 76 meters. Find the length of the garden.
a. 23 meters
b. 76 meters
c. 345 meters
d. 15 meters
6. The perimeter of a triangle is 30 inches. The length of the middle side is 2 inches more than the length of the smaller side and the largest side is 4 inches more than twice the length of the smallest side. Find the length of the smallest side.
a. 6 inches
b. 8 inches
c. 4 inches
d. 2 inches
7. If 8 times a number is increased by 20, the result is 26 less than the square of the number. Choose the equation that could be used to find this number, x.
a. 
b. 
c. 
d. 
8. Identify the proportion listed below that solves the problem: A car can travel 603 miles on 11 gallons of gasoline. How far can the car travel on 36 gallons?
a. 
c. 
b. 
d. 
9. Two cars start from the same point and travel in opposite directions. The rate of the slower car is 15 miles per hour less than the rate of the faster car. After 8 hours they are 840 miles apart. Find the speed of the cars.
a. 90 mph and 75 mph
b. 105 mph and 90 mph
c. 60 mph and 45 mph
d. 100 mph and 85
10. If a student completed this worksheet that covers word problems that are on the state competency exam to pass this class and had some difficulty. Should the student make sure that they ask questions, always go to class, take good notes, complete their homework, and seek extra help when needed?
a. Yes
b. Yes
c. Yes
d. Yes
Answers to Word Problem Lab for MAT0024C
1. A
To find the discount you multiply the original price by the percent of the discount.
So, the discount is $50.00(0.25) = $12.50.
To find the sale price you subtract the original price from the discount.
So, to find the sale price you take 50.00 – 12.50 = 37.50. The sale price is $37.50.
________________________________________________________________________
2. D Check
Original Cost – Discount = Sale Price 478.46 - .35(478.46) = 311
X - .35X = 311 478.46 – 167.46 = 311
1X - .35X = 311 311 = 311
.65X = 311
.65 .65
X = 478.46
________________________________________________________________________
3. D
Original Cost + Increase = New Price Check: 235.39 + .30(235.39) = 306
X + .30X = 306 235.39 + 70.61 = 306
1X + .30X = 306
306 = 306
1.30X = 306
1.30 1.30
X = $235.39
________________________________________________________________________
4. B
The formula to find simple interest is: Interest = Principal x Rate x Time (I = P*R*T)
The information gives would lead to: 200 = X (0.05) (8)
Then simplify: 200 = X(0.4)
Then solve for x by dividing both sides by 0.4: 200/0.04 = X(0.04)/0.04
X = $500.00, the principal (amount to be invested) is $500.00.
Check: 200 = 500(0.05)(8)
200 = 200
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5. A
Width: W
W + 8 Length: W + 8
Perimeter: 76
W W
W + 8
Equation: W + W + 8 + W + W + 8 = 76 Width: W = 15
Combine Like Terms: 4W + 16 = 76 Length: 15 + 8 = 23
- 16 - 16
4W = 60 Check: 15 + 23 + 15 + 23 = 76
4 4 76 = 76
Solve: W = 15
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6. A
Small: X
Middle: X + 2
Large: 2X + 4 X X + 2
Perimeter: 30
2X + 4
The equation will be: X + X + 2 + 2X + 4 = 30
Combine like terms: 4X + 6 = 30
Solve: - 6 - 6
4X = 24 Check: 6 + 6 + 2 + 2(6) + 4 = 30
4 4 6 + 8 + 16 = 30
14 + 16 = 30
X = 6 30 = 30
Small: X = 6
Middle: 6 + 2 = 8
Large: 2(6) + 4 = 16
________________________________________________________________________
7. B
Translate the problem to:
________________________________________________________________________
8. A
Note: If your proportion does not match the
proportion
on the test, multiply the
diagonals to see which matches.
Matches:
________________________________________________________________________
9. C
|
Type |
D |
R |
T |
|
Fast Car |
8X |
X |
8 |
|
Slow Car |
8(X – 15) |
X – 15 |
8 |
|
Total |
840 |
|
|
Fill in the 4 x 4 chart with the given information.
To fill in the distance column use the formula Distance = Rate x Time
You now have the formula:
8X + 8(X – 15) = 840
Distributive Property: 8X + 8X – 120 = 840
Combine Like Terms: 16X -120 = 840
+ 120 +120
Solve for X: 16X = 960
16 16
X = 60
Substitute X into the chart and answer the question:
|
Type |
D |
R |
T |
|
Fast Car |
8(60) = 480 miles |
60 mph |
8 |
|
Slow Car |
8(60– 15) = 360 miles |
60 – 15 = 45 mph |
8 |
|
Total |
840 miles |
|
|
________________________________________________________________________
10. UMMMMMMMMMMMMMMMMM!!!!!!! The answer is YES!!!
The competency exam is very important. To pass MAT0024C Elementary Algebra you need an 80% or better on the competency exam.
Note: Use test taking strategies like eliminating the incorrect answers first, then look at the possible choices.
How do you solve word problems?
______________________________________________________________________________
______________________________________________________________________________
Section 2.5: Problem Solving Practice Problems
1. A CD is priced at $15.00, but it is on sale for 20% off. What is the sale price of the CD?
a. $3.00
b. $10.00
c. $18.00
d. $12.00
2. If a sony play station costs $250 after a 15% discount, what was the original cost?
e. $294.12
f. $212.50
g. $287.50
h. $399.46
3. If a palm pilot costs $1300 after a 20% increase in price, what was the original cost?
a. $1625.00
b. $1083.33
e. $1560.00
f. $1040.00
4. Find the simple interest percent if you invested $1000.00 for 5 years and you received $500.00 in interest.
a. 20%
b. 50%
c. 10%
d. 40%
5. The width of a rectangular garden is 8 meters less than its length. Its perimeter is 76 meters. Find the length of the garden.
e. 23 meters
f. 76 meters
g. 345 meters
h. 15 meters
6. The perimeter of a triangle is 51 inches. The length of the middle side is 5 inches more than the length of the smaller side and the largest side is 4 inches less than three times the length of the smallest side. Find the length of the middle side.
e. 10 inches
f. 15 inches
g. 26 inches
h. 5 inches
7. If 10 times a number is decreased by 29, the result is the product of 42 and the square of the number. Choose the equation that could be used to find this number, x.
e. 
f. 
g. 
h. 
8. Identify the proportion listed below that solves the problem: A car can travel 1200 miles on 60 gallons of gasoline. How many gallons do you need to travel 100 miles?
a. 
c.
b. 
d.
9. Two shrimp boats start from the same port at the same time, but they head in opposite directions. The slower boat travels 15 knots per hour slower than the fast boat. At the end of 12 hours, they were 600 nautical miles apart. How many nautical miles had the slow boat traveled by the end of the 12-hour period?
a. 210 nautical miles
b. 17.5 nautical miles
c. 2.5 nautical miles
d. 390 nautical miles
10. If a student had some difficulty completing this worksheet that covers word problems that are on the state competency exam, that is REQUIRED to pass this class and the student wanted to do well on the competency exam, what should the student do?
a. Ask questions
b. Always go to class and take good notes
c. Complete their homework
d. Seek extra help when needed like the instructor and the tutoring center (1-131)
e. ALL THE ABOVE!!!!
Answers to Section 2.5: Problem Solving Practice Problems
1. D
To find the discount you multiply the original price by the percent of the discount.
So, the discount is $15.00(0.20) = $3.00.
To find the sale price you subtract the original price from the discount.
So, to find the sale price you take 15.00 – 3.00 = 12.00. The sale price is $12.00.
________________________________________________________________________
2. A Check
Original Cost – Discount = Sale Price 294.12 - .15(294.12) = 250
X - .15X = 250 294.12 – 44.12 = 250
1X - .15X = 250 250 = 250
.85X = 250
.85 .85
X = 294.12
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3. B
Original Cost + Increase = New Price Check: 1083.33 + .20(1083.33) = 1300
X + .20X = 1300 1083.33 + 216.67 = 1300
1X + .20X = 1300
1300 = 1300
1.20X = 1300
1.20 1.20
X = $1083.33
________________________________________________________________________
4. C
The formula to find simple interest is: Interest = Principal x Rate x Time (I = P*R*T)
The information gives would lead to: 500 = (1000)X (5)
Then simplify: 500 = X(5000)
Then solve for x by dividing both sides by 5000: 500/5000 = X(5000)/5000
X = 0.10, the simple interest percent would be 10%.
Check: 500 = 1000(0.10)(5)
500 = 500
________________________________________________________________________
5. A
W - 8 Width: W -8
Length: W
W W
Perimeter: 76
W - 8
Equation: W + W - 8 + W + W - 8 = 76 Width: 23 – 8 = 15
Combine Like Terms: 4W - 16 = 76 Length: 23
+ 16 +16
4W = 92 Check: 15 + 23 + 15 + 23 = 76
4 4 76 = 76
Solve: W = 23
________________________________________________________________________
6. B
Small: X
Middle: X + 5
Large: 3X - 4 X X + 5
Perimeter: 51
3X - 4
The equation will be: X + X + 5 + 3X - 4 = 51
Combine like terms: 5X + 1 = 51
Solve: - 1 - 1
5X = 50 Check: 10 + 10 + 5 + 3(10) - 4 = 51
5 5 10 + 15 + 26 = 51
25 + 26 = 51
X = 10 51 = 51
Small: X = 10
Middle: 10 + 5 = 15
Large: 3(10) - 4 = 26
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7. B
Translate the problem to:
________________________________________________________________________
8. B
Note: If your proportion does not match the
proportion
on the test, multiply the
diagonals to see which matches.
________________________________________________________________________
9. A
|
Type |
D |
R |
T |
|
Fast Boat |
12X |
X |
12 |
|
Slow Boat |
12(X-15) |
X |
12 |
|
Total |
600 |
|
|
Fill in the 4 x 4 chart with the given information.
To fill in the distance column use the formula Distance = Rate x Time
You now have the formula:
12X + 12(X - 15) = 600
Distributive Property: 12X + 12X -180 = 600
Combine Like Terms: 24X - 180 = 600
+180 +180
Solve for X: 24X = 780
24 24
X = 32.5
Substitute X into the chart and answer the question:
|
Type |
D |
R |
T |
|
Fast Boat |
12(32.5) =390 miles |
32.5 knots |
12 |
|
Slow Boat |
12(32.5-15) = 210 miles |
32.5-15 = 17.5 knots |
12 |
|
Total |
600 miles |
|
|
The answer from the chart is the slow boat traveled 210 miles.
________________________________________________________________________
10. UMMMMMMMMMMMMMMMMM!!!!!!! The answer is E!!!
The competency exam is very important.
To pass MAT0024C Elementary Algebra you need an 80% or better on the competency exam.
Note: Use test taking strategies like eliminating the incorrect answers first, then look at the possible choices.